Study of the 3D Coronal Magnetic Field of Active Region 11117 Around the Time of a Confined Flare Using a Data-Driven CESE-MHD Model

Non-potentiality of the solar coronal magnetic field accounts for the solar explosion like flares and CMEs. We apply a data-driven CESE-MHD model to investigate the three-dimensional (3D) coronal magnetic field of NOAA active region (AR) 11117 around the time of a C-class confined flare occurred on 2010 October 25. The CESE-MHD model, based on the spacetime conservation-element and solution-element scheme, is designed to focus on the magnetic-field evolution and to consider a simplified solar atomsphere with finite plasma β. Magnetic vector-field data derived from the observations at the photoshpere is inputted directly to constrain the model. Assuming that the dynamic evolution of the coronal magnetic field can be approximated by successive equilibria, we solve a time sequence of MHD equilibria basing on a set of vector magnetograms for AR 11117 taken by the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamic Observatory (SDO) around the time of flare. The model qualitatively reproduces the basic structures of the 3D magnetic field, as supported by the visual similarity between the field lines and the coronal loops observed by the Atmospheric Imaging Assembly (AIA), which shows that the coronal field can indeed be well characterized by the MHD equilibrium in most time. The magnetic configuration changes very limited during the studied time interval of two hours. A topological analysis reveals that the small flare is correlated with a bald patch (BP, where the magnetic field is tangent to the photoshpere), suggesting that the energy release of the flare can be understood by magnetic reconnection associated with the BP separatrices. The total magnetic flux and energy keep increasing slightly in spite of the flare, while the magnetic free energy drops during the flare with an amount of 1.7 × 10³⁰ erg, which can be interpreted as the energy budget released by the minor C-class flare.